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Conformal FourthRank Gravity  Victor Tapia
; A.L. Marrakchi
; M. Cataldo
;  Date: 
3 Mar 1993  Subject:  grqc  Abstract:  We consider the consequences of describing the metric properties of space time through a quartic line element $ds^4=G_{mu
ulambda
ho}dx^mu dx^
u dx^lambda dx^
ho$. The associated "metric" is a fourthrank tensor $G_{mu
ulambda
ho}$. We construct a theory for the gravitational field based on the fourthrank metric $G_{mu
ulambda
ho}$ which is conformally invariant in four dimensions. In the absence of matter the fourthrank metric becomes of the form $G_{mu
ulambda
ho}=g_{(mu
u}g_{lambda
ho )}$ therefore we recover a Riemannian behaviour of the geometry; furthermore, the theory coincides with General Relativity. In the presence of matter we can keep Riemannianicity, but now gravitation couples in a different way to matter as compared to General Relativity. We develop a simple cosmological model based on a FRW metric with matter described by a perfect fluid. Our field equations predict that the entropy is an increasing function of time. For $k_{obs}=0$ the field equations predict $Omegaapprox 4y$, where $y={pover
ho}$; for $Omega_{small}=0.01$ we obtain $y_{pred}=2.5 imes 10^{3}$. $y$ can be estimated from the mean random velocity of typical galaxies to be $y_{random}=1 imes10^{5}$. For the early universe there is no violation of causality for $t>t_{class}approx10^{19}t_{Planck}approx 10^{24}s$.  Source:  arXiv, grqc/9303009  Other source:  [GID 787470] grqc/9303009  Services:  Forum  Review  PDF  Favorites 


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